** Company: ** DRDO

1. The state space equation of the circuit shown in given figure for x1=v0, x2=I is

2. The open loop gain of a unity feedback system is G(s)=wn^2 / s(s+2wn). The unit step response c(t) of the system is

3. The angles of the asymptotes of the root loci of the equation s^3 + 5s^2 + (K+2)s + K = 0, for 0<=K<8, are a) 0 and 270 b) 0 and 180 c) 90 and 270 d) 90 and 180 4. The bode plot corresponding to a proportional derivative controller is the one shown in given figure 5. In frequency modulation, the instantaneous a) amplitude of the carrier signal is varied with the instantaneous amplitude of the message signal b) amplitude of the carrier signal is varied with the instantaneous frequency of the message signal c) frequency of the carrier signal is varied with the instantaneous amplitude of the message signal d) frequency of the carrier signal is varied with the instantaneous frequency of the message signal 6. If X is a zero mean Gaussian random variable, then P{X<=0} is a) 0 b) 0.25 c) 0.5 d) 1 7. If a single-tone amplitude modulated signal at a modulation depth of 100% transmits a total power of 15W, the power in the carrier component is a) 5W b) 10W c) 12W d) 15W 8. In a superheterodyne receiver, rejection of the image signal can be achieved by using a a) higher local oscillatorn frequency b) crystal oscillator c) narrow band IF filter d) narrow band filter at RF stage 9. The number of bbits per sample of a PCM system depends upon the a) sampler type b) quantizer type c) number of levels of the quantizer d) sampling rate 10. Which one of the following is used for the detection of AM-DSB-SC signal a) Ratio detector b) Foster-Seeley discriminator c) Product demodulator d) Balanced-slpoe detector 11. Which one of the following signal pairs can represent a BPSK signal a) A cos2pfct, A sinpfct b) A cos2pfct, - A sinpfct c) - A cos2pfct, A sinpfct d) A sin2pfct, A cospfct 12. Which one of the following can be used for the detection of the noncoherent BPSK signal a) matched filter b) phase-locked loop c) envelope detector d) product demodulator 13. Bits of duration Tb are to be transmitted using a BPSK modulation with a carrier of frequency Fc Hz. The power spectral density of the transmitted signal has the first null at the normalized frequency a) |F – Fc|Tb = 0 b) |F – Fc|Tb = 1 c) |F – Fc|Tb = 2 d) |F – Fc|Tb = 4 14. The probability of bit error of a BPSK modulation scheme, with transmitted signal energy per bit Eb, in an additive white Gaussian noise channel having one-sided power spectral density N0, is a) (1/2) erfc(Eb/2N0) b) (1/2) erfcv(Eb/2N0) c) (1/2) erfc(Eb/N0) d) (1/2) erfcv (Eb/N0) 15. For a given transmitted pulse p(t), 0<=t<=T, the impulse response of a filter matched to the received signal is a) –p(t-T), 0<=t<=T b) –p(T-t), 0<=t<=T c) p(t-T), 0<=t<=T d) p(T-t), 0<=t<=T 16. The multiple access communication scheme in which each user is allocated the full available channel spectrum for a specified duration of time is known as a) CDMA b) FDMA c) TDMA d) MC-CDMA 17. GSM system uses TDMA with a) 32 users per channel b) 16 users per channel c) 8 users per channel d) 4 users per channel 18. If Rx(t) is the auto-correlation function of a zero-mean wide-sense stationary random process X, then which one of the following is NOT true? a) Rx(t) = Rx(-t) b) Rx(t) = -Rx(-t) c) sx^2 = Rx(0) d) |Rx(t)| <=Rx(0) 19. If E denotes the expectation operator, then E[X-EX]^3 of a random variable X is a) EX^3 – E^3X b) EX^3 + 2E^3X – 3EX Ex^2 c) 3EX^3 – E^3X d) 2EX^3 + E^3X – 3EX EX^2 20. A discrete memoryless source produces symbols m1,m2,m3 and m4 with probabilities 1/2, 1/4 , 1/8 and 1/8, respectively. The entropy of the source is a) ¼ b) 1 c) 7/4 d) 2 21. A channel has a signal-to-noise ratio of 63 and bandwidth of 1200 Hz. The maximum data rate that can be sent through the channel with arbitrary low probability of error is a) 600 bps b) 1200 bps c) 4800 bps d) 7200 bps 22. For the vectors A = X ax + Y ay and B = Z az, del . (A X B) is a) 0 b) 1 c) XZ d) YZ 23. Which one of the following relations represents Strokes’ theorem (symbols have their usual meaning)? a) ?s del X A.ds = 0 b) ?L A.dl = ?s del X A.ds c) ?s A X dS = -?v (del X A)dv d) ?v del.Adv = ?s A.ds 24. Which one of the following relations is not correct (symbols have their usual meaning)? a) del X E = - ?B/?t b) del X H = J + ?E/?t c) del.D = ?v d) del.B = 0 25. The electric field component of a uniform plane wave propagating in a lossless magnetic dielectric medium is given by E(t,z)=ax 5cos(10^9 t – 20/3 z)V/m. If ?0 represents the intrinsic impedance of the free space, the corresponding magnetic field component is given by a) H(t,z)= ay 5/2 ?0 cos(10^9t – 20/3 z)A/m b) H(t,z)= ay 10/ ?0 cos(10^9t – 20/3 z)A/m c) H(t,z)= az 5/2 ?0 cos(10^9t – 20/3 z)A/m d) H(t,z)= az 10/ ?0 cos(10^9t – 20/3 z)A/m 26. The skin depth of a non-magnetic conducting material at 100 MHz is 0.15 mm. The distance which a plane wave of frequency 10 GHz travels in this material before its amplitude reduces by a factor of e^-1 is a) 0.0015 mm b) 0.015 mm c) 0.15 mm d) 1.5 mm 27. A lossless transmission line has a characteristic impedance of 100 ohms and an inductance per unit length of 1 µH/m. If the line is operated at 1 GHz, the propagation constant ß is a) 2p rad/m b) 20p/3 rad/m c) 20p rad/m d) 2p *10^5 rad/m 28. When a load resistance Rl is connected to a lossless transmission line of characteristic impedance 75 ohms, it results in a VSWR of 2. The load resistance is a) 100 ohms b) 75v2 ohms c) 120 ohms d) 150 ohms 29. A two-port network characterized by the S-parameter matrix, [S] = [0.3 L0 0.9 L90 0.9 L90 0.2 L0] Is a) both reciprocal and lossless b) reciprocal, but not lossless c) lossless, but not reciprocal d) neither reciprocal nor lossless 30. A lossless air filled rectangular waveguide has internal dimensions of a cm * b cm. If a=2b and the cutoff frequency of the TE02 mode is 12 GHz, the cutoff frequency of the dominant mode is a) 1 GHz b) 3 GHz c) 6 GHz d) 9 GHz 31. A Hertzian dipole antenna is placed at the origin of a coordinate system and it is oriented along z-axis. In which one of the following planes the radiation pattern of the antenna has a circular shape? a) x=0 b) y=0 c) z=0 d) ø=45 32. Which one of the following statements is not true? a) Antenna losses are taken into account in calculating its power gain b) For an antenna which does not dissipate any power, the directive gain and the power gain are equal c) Directivity of an antenna is the maximum value of its directive gain d) The directive gain of a Hertzian dipole is same in all direction 33. The directivity of a half dipole antenna is a) 1.0 b) 1.5 c) 1.64 d) 2 34. Which one of the following is not true for a step index optical fibre? a) It can support multiple modes b) HE11 mode is its lowest order mode c) The refractive index of the cladding is higher than that of the core d) At a given wavelength, single mode operation is possible by proper choice of core diameter, core and cladding refractive indices.